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Abstract

We consider the problem of digital communication in a Rayleigh flat fading environment using a multiple antenna system, when both the transmitter and the receiver are unaware of the channel coefficients. Using Stein's lemma to bound the pairwise error probabilities, we propose to use the Kullback-Leibler distance between distributions assigned to the transmitted symbols to design space-time constellations for non-coherent communication. We show that optimal codes according to the proposed criterion can be obtained by partitioning the signal space into appropriate subsets and using unitary designs inside each subset. Actual constellation design is performed by solving an optimization problem to find the size and location of the subsets. Our simulation results show that the new constellations can provide a substantial improvement in the performance over known unitary space-time codes. Furthermore, the proposed constellations can be decoded using a simple low-complexity decoder.